Hi Havsurf,
NSD will reduce inflammation which will make it easier to heal your gut. Apple cider vinegar won't do to much in healing your gut, but just make your stomach more acidic as it should be, it improved digestion. I never really took apple cider to heal my gut, you can take acidic probiotic drinks instead (water kefir and/or kombucha), they will have the same affect, but also include lots of good bacteria/enzymes.
Hydrogen Peroxide will help kill a lot of the bad bacteria (including Klebsiella), but also help the good bacteria to grow. I had one guy tell me his AS was so bad he was in bed the whole summer, but after he took peroxide it made a massive difference and shortly after he was running.
For me, the probiotics & peroxide alone helped a lot, but the final cure came when I also introduced slow cooking/bone broths. If you can do that with healthy meat (pasture fed or wild caught seafood), it shouldn't be long before you will heal your gut.